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Question 1199962: If a poll percent in within 3% of the true percent p, and the poll percent is 31%, describe the possible values of p:
a. using a double inequality;
b. using absolute value.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the poll percent is 31%.
the true percent is p.
a. using a double inequality.
p = 31% plus or minus 3%.
this tells you that p will be between 28% and 34%.
b. using absolute value.
absolute value of (31% - p) = 3%
if (31% - p) is positive, you get (31% - p) = 3%.
solve for p to get p = 31% - 3% = 28%
if (31% - p) is negative, you get -(31% - p) = 3% which becomes -31% + p = 3%.
solve for p to get p = 3% + 31% = 34%
this tells you that p will be between 28% and 34%.
the reason for this is because the absolute value of the expression has to be positive.
if it is positive, then the absolute value of it is already positive.
if it is negative, then the absolute value of it is multiplied by -1 to make it positive.
example:
the absolute value of 5 is equal to 5.
the absolute value of -5 is equal to -(-5) which is equal to 5.
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